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1.
A thermodynamic approach to the construction of a phenomenological macroscopic model of developed turbulence in a compressible fluid is considered with regard for the formation of space–time dissipative structures. A set of random variables were introduced into the model as internal parameters of the turbulent–chaos subsystem. This allowed us to obtain, by methods of nonequilibrium thermodynamics, the kinetic Fokker–Planck equation in the configuration space. This equation serves to determine the temporary evolution of the conditional probability distribution function of structural parameters pertaining to the cascade process of fragmentation of large-scale eddies and temperature inhomogeneities and to analyze Markovian stochastic processes of transition from one nonequilibrium stationary turbulent-motion state to another as a result of successive loss of stability caused by a change in the governing parameters. An alternative method for investigating the mechanisms of such transitions, based on the stochastic Langevin-type equation intimately related to the derived kinetic equation, is also considered. Some postulates and physical and mathematical assumptions used in the thermodynamic model of structurized turbulence are discussed in detail. In particular, we considered, using the deterministic transport equation for conditional means, the cardinal problem of the developed approach—the possibility of the existence of asymptotically stable stationary states of the turbulent-chaos subsystem. Also proposed is the nonequilibrium thermodynamic potential for internal coordinates, which extends the well-known Boltzmann–Planck relationship for equilibrium states to the nonequilibrium stationary states of the representing ensemble. This potential is shown to be the Lyapunov function for such states. The relation is also explored between the internal intermittence in the inertial interval of scales and the fluctuations of the energy of dissipation. This study is aimed at constructing representative models of natural space environments. It develops a synergetic approach to modeling the structurized turbulence of astrophysical and geophysical systems, which was proposed by the author in previous papers (Kolesnichenko, 2002, 2003). 相似文献
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Zdeněk Kopal 《Astrophysics and Space Science》1968,1(4):411-423
The aim of the present paper will be to investigate the circumstances under which an irreversible dissipation of the kinetic energy into heat is generated by the dynamical tides in close binary systems if (a) their orbit is eccentric; (b) the axial rotation of the components is not synchronized with the revolution; or (c) the equatorial planes are inclined to that of the orbit.In Section 2 the explicit form of the viscous dissipation function will be set up in terms of the velocity-components of spheroidal deformation arising from the tides; in Section 3, the principal partial tides contributing to the dissipation will be detailed; Section 4 will be devoted to a determination of the extent of stellar viscosity — both gas and radiative; while in the concluding Section 5 quantitative estimates will be given of the actual rate at which the kinetic energy of dynamical tides gets dissipated into heat by viscous friction in stellar plasma.The results disclose that the amount of heat produced per unit time by tidal interaction between components of actual close binaries equals only about 10–10th part of their nuclear energy production; and cannot, therefore, affect the internal structure of evolution of the constituent stars to any appreciable extent. Moreover, it is shown that the kinetic energy of their axial rotation can be influenced by tidal friction only on a nuclear, rather than gravitational (Kelvin) time-scale — as long as plasma or radiative viscosity constitute the sole sources of dissipation. However, the emergence of turbulent viscosity in secondary components of late spectral types, which have evolved away from the Main Sequence, can accelerate the dissipation 105–106 times, and thus give rise to appreciable changes in the elements of the system (particularly, in the orbital periods) over time intervals of the order of 105–106 years. Lastly, it is pointed out that, in close binary systems consisting of a pair of white dwarfs, a dissipation of the kinetic energy through viscous tides in degenerate fermion-gas could produce enough heat to account, by itself, for the observed luminosity of such objects. 相似文献
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We formulate a two-stage scheme for astrophysical turbulence in the frame of a revised Kolmogorov self-similar theory, hierarchical in nature. According to this approach, graviaation is revealed to be the main source of dissipated energy supporting the turbulent cascade. Results are compared with observational data about molecular clouds in the Galaxy and with the forecastings of an intermittent model of the same authors. 相似文献
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A. V. Kolesnichenko 《Solar System Research》2010,44(4):334-347
This paper considers the modern approach to the thermodynamic modeling of developed turbulent flows of a compressible fluid
based on the systematic application of the formalism of extended irreversible thermodynamics (EIT) that goes beyond the local
equilibrium hypothesis, which is an inseparable attribute of classical nonequilibrium thermodynamics (CNT). In addition to
the classical thermodynamic variables, EIT introduces new state parameters—dissipative flows and the means to obtain the respective
evolutionary equations consistent with the second law of thermodynamics. The paper presents a detailed discussion of a number
of physical and mathematical postulates and assumptions used to build a thermodynamic model of turbulence. A turbulized liquid
is treated as an indiscrete continuum consisting of two thermodynamic sub-systems: an averaged motion subsystem and a turbulent
chaos subsystem, where turbulent chaos is understood as a conglomerate of small-scale vortex bodies. Under the above formalism,
this representation enables the construction of new models of continual mechanics to derive cause-and-effect differential
equations for turbulent heat and impulse transfer, which describe, together with the averaged conservations laws, turbulent
flows with transverse shear. Unlike gradient (noncausal) relationships for turbulent flows, these differential equations can
be used to investigate both hereditary phenomena, i.e., phenomena with history or memory, and nonlocal and nonlinear effects.
Thus, within EIT, the second-order turbulence models underlying the so-called invariant modeling of developed turbulence get
a thermodynamic explanation. Since shear turbulent flows are widespread in nature, one can expect the given modification of
the earlier developed thermodynamic approach to developed turbulence modeling (see Kolesnichenko, 1980; 1998; 2002–2004; Kolesnichenko
and Marov, 1985; Kolesnichenko and Marov, 2009) to be used in research on a broad class of dissipative phenomena in various
astro- and geophysical applications. In particular, a major application of the proposed approach is the reconstruction of
the processes in the preplanetary circumsolar disk, which might help solve the fundamental problems of stellar-planetary cosmogony. 相似文献
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M. N. Izakov 《Solar System Research》2005,39(1):33-44
Based on spaceborne experimental data, characteristics of turbulence are calculated for the Venusian troposphere under conditions corresponding to the planet-averaged flux of solar radiation, which is equal to its value at a solar zenith angle of 66°. Additionally, given experimental data on radiation fluxes and their numerical calculations, turbulence characteristics were calculated for a solar zenith angle of 45°. The turbulence pattern is significantly different for small and large solar zenith angles. At large solar zenith angles, there exist an anomalous downward turbulent heat flux above 7–10 km and a normal upward flux at lower heights. At small zenith angles, the turbulent flux is normal throughout the entire troposphere. The dissipation of turbulent energy contributes significantly to the atmospheric heating in a wide range of altitudes. The spectrum of the time and space scales of dissipative processes in the troposphere is very wide and changes with height.Translated from Astronomicheskii Vestnik, Vol. 39, No. 1, 2005, pp. 38–50.Original Russian Text Copyright © 2005 by Izakov. 相似文献
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Robert Selkowitz Eric G. Blackman 《Monthly notices of the Royal Astronomical Society》2007,382(3):1119-1123
We consider the dissipation by Fermi acceleration of magnetosonic turbulence in the Reynolds layer of the interstellar medium. The scale in the cascade at which electron acceleration via stochastic Fermi acceleration (STFA) becomes comparable to further cascade of the turbulence defines the inner scale. For any magnetic turbulent spectra equal to or shallower than Goldreich–Sridhar this turns out to be ≥1012 cm, which is much larger than the shortest length-scales observed in radio scintillation measurements. While STFA for such spectra then contradict models of scintillation which appeal directly to an extended, continuous turbulent cascade, such a separation of scales is consistent with the recent work of Boldyrev & Gwinn and Boldyrev & Konigl suggesting that interstellar scintillation may result from the passage of radio waves through the Galactic distribution of thin ionized boundary surfaces of H ii regions, rather than density variations from cascading turbulence. The presence of STFA dissipation also provides a mechanism for the non-ionizing heat source observed in the Reynolds layer of the interstellar medium. STFA accommodates the proper heating power, and the input energy is rapidly thermalized within the low-density Reynolds layer plasma. 相似文献
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Eric G. Blackman George B. Field 《Monthly notices of the Royal Astronomical Society》2008,386(3):1481-1486
The magnetic Reynolds number, R M , is defined as the product of a characteristic scale and associated flow speed divided by the microphysical magnetic diffusivity. For laminar flows, R M also approximates the ratio of advective to dissipative terms in the total magnetic energy equation, but for turbulent flows this latter ratio depends on the energy spectra and approaches unity in a steady state. To generalize for flows of arbitrary spectra we define an effective magnetic dissipation number, R M,e , as the ratio of the advection to microphysical dissipation terms in the total magnetic energy equation, incorporating the full spectrum of scales, arbitrary magnetic Prandtl numbers, and distinct pairs of inner and outer scales for magnetic and kinetic spectra. As expected, for a substantial parameter range R M,e ∼ O (1) ≪ R M . We also distinguish R M,e from where the latter is an effective magnetic Reynolds number for the mean magnetic field equation when a turbulent diffusivity is explicitly imposed as a closure. That R M,e and approach unity even if R M ≫ 1 highlights that, just as in hydrodynamic turbulence, energy dissipation of large-scale structures in turbulent flows via a cascade can be much faster than the dissipation of large-scale structures in laminar flows. This illustrates that the rate of energy dissipation by magnetic reconnection is much faster in turbulent flows, and much less sensitive to microphysical reconnection rates compared to laminar flows. 相似文献
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In previous publications the author considered how breaking buoyancy waves and the thermal source arising due to different absorption coefficients of solar and atmospheric radiation fluxes contributed to turbulence. In this study, the contribution to turbulence made by the dynamical source arising in consequence of convective instability of large-scale atmospheric motions is examined. Its value is estimated from experimental wind speed data for the atmosphere of Venus. The contributions of the indicated sources of turbulent energy are compared. The rate of dissipation of kinetic energy due to molecular viscosity is demonstrated to be several orders of magnitude less than the rate of dissipation necessary to maintain an invariable superrotation pattern. This is an additional argument for the permanent existence of turbulence in the atmosphere of Venus, which many authors consider doubtful. It is demonstrated why turbulence is present at the atmospheric stratification that seems to be stable. 相似文献
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A. V. Kolesnichenko 《Solar System Research》2008,42(5):391-404
A stochastic-thermodynamic approach to the derivation of the generalized fractional Fokker—Planck—Kolmogorov (FFPK) equations
is considered. The equations describe turbulent transfer processes in a subsystem of turbulent chaos on the basis of fractional
dynamics, which takes into account the structure and metric of fractal time. The actual turbulent motion of a fluid is known
to be intermittent, since it demonstrates the properties that are intermediate between the properties of regular and chaotic
motions. On the other hand, the process of the flow turbulization may be non-Markovian because of the multidimensional spatiotemporal
correlations of pulsating parameters; in a physical language, this means that the process has a memory. The introduction of
fractional time derivatives into the FFPK kinetic equations, used to find the probability distribution functions for different
statistical characteristics of structured turbulence, makes it possible to use an unified mathematical formalism in considering
the effects of memory, nonlocality, and time intermittence, with which we usually associate the presence of turbulent bursts
against the background of less intense low-frequency oscillations in the background turbulence. This study is aimed at creating
representative models of space and natural media. It is a development of the synergetic approach to the modeling of structured
turbulence in astrogeophysical systems, which has been developed by the author in a series of papers (Kolesnichenko, 2002–2005). 相似文献
11.
We suggest that the solar corona is stationarily heated by Joule dissipation of magnetohydrodynamic (MHD) turbulence. This turbulence is continuously being fed by subphotospheric convective motions at very low wavenumbers where the plasma can be considered ideal. The cascade process due to the nonlinear interaction of the turbulent modes, effectively transfers energy to even shorter wavenumbers until Joule effect becomes dominant and converts the cascading magnetic energy into heat.Assuming that a stationary spectrum is established, we show that MHD turbulence naturally provides a way of enhancing the Joule dissipation of macroscopic magnetic stresses and a heating rate can be derived. 相似文献
12.
The decay of kinetic helicity is studied in numerical models of forced turbulence using either an externally imposed forcing function as an inhomogeneous term in the equations or, alternatively, a term linear in the velocity giving rise to a linear instability. The externally imposed forcing function injects energy at the largest scales, giving rise to a turbulent inertial range with nearly constant energy flux while for linearly forced turbulence the spectral energy is maximum near the dissipation wavenumber. Kinetic helicity is injected once a statistically steady state is reached, but it is found to decay on a turbulent time scale regardless of the nature of the forcing and the value of the Reynolds number (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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When the velocity field of a magneto-fluid is accorded an intrinsically equal status with the magnetic field, standard magnetohydrodynamics (MHD) must be replaced by the dispersive or Hall MHD which retains some crucial two-fluid effects, in particular the physics on the ion skin depth scale. The larger system has three quadratic invariants: the generalized helicity (a sum of the cross and fluid helicities) is added to the ranks of the standard total energy and the magnetic helicity invariants. Based on this extended set, dimensional arguments à la Kolmogorov are invoked to derive the turbulent spectral distributions of the kinetic and the magnetic energy densities in the inertial range. By using the selective dissipation hypothesis, we construct the spectra on three different scales within the inertial range, and acknowledge the possible role of the dual cascade of the kinetic and the magnetic energy densities. The additional structure imparted to the spectral laws (by the inclusion of the generalized helicity) allows us to reproduce, remarkably well, the essentials as well as details of the observed spectra of the motions and of the magnetic fields of the solar atmosphere on the scales of a few thousand km. 相似文献
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The scenario of magnetohydrodynamic turbulence in connection with coronal active regions has been actively investigated in recent years. According to this viewpoint, a turbulent regime is driven by footpoint motions and the incoming energy is efficiently transferred to small scales due to a direct energy cascade. The development of fine scales to enhance the dissipation of either waves or DC currents is therefore a natural outcome of turbulent models. Numerical integrations of the reduced magnetohydrodynamic equations are performed to simulate the dynamics of coronal loops driven at their bases by footpoint motions. These simulations show that a stationary turbulent regime is reached after a few photospheric times, displaying a broadband power spectrum and a dissipation rate consistent with the energy loss rates of the plasma confined in these loops. Also, the functional dependence of the stationary heating rate with the physical parameters of the problem is obtained, which might be useful for an observational test of this theoretical framework. 相似文献
15.
The paper is concerned with turbulent flow of incompressible, spatially homogeneous viscous fluid. A model for turbulence energy equation is obtained, ignoring the pressure redistribution term in dynamical equations for the Reynolds stresses. The mechanism of dissipation on turbulence production is discussed and shown that the turbulence kinetic energy decays upto a constant value as time becomes infinitely large, i.e., for isotropy, dissipation inhibits the production process and if
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initially then dissipation causes reduction in anisotropy. 相似文献
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磁重联在宇宙的许多动力学现象中都是非常核心的过程.磁流体动力学(MHD)数值模拟是研究磁重联过程以及相应物理图像的一种很有效的手段.通过不同的参数组合,来研究MHD数值模拟中磁雷诺数和空间分辨率对磁重联率、数值耗散和能谱分布的影响.对得到的数据进行分析后,发现磁雷诺数对磁重联率和能谱分布有一定的影响.磁雷诺数越大,磁重联过程进入非线性阶段所需的特征时间越短,磁重联率就越早发生跃升.磁雷诺数Rm对耗散开始发挥作用的Kolmogorov微观尺度lko有明显影响:Rm越大,lko就越小.研究了磁重联过程中包括数值耗散在内的额外耗散对重联过程的影响.结果表明,撕裂模不稳定性开始之前的额外耗散以纯数值耗散为主,撕裂模不稳定性出现之后,额外耗散出现同步跃升,说明不稳定性导致的湍流明显增强了耗散的效果,相当于在局部湍流区引入了超电阻.能谱分析进一步表明,大尺度电流片的lko完全可能出现在宏观的MHD尺度上. 相似文献
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This paper considers, in the context of modeling the evolution of a protoplanetary cloud, the hydrodynamic aspects of the theory of concurrent processes of mass transfer and coagulation in a two-phase medium in the presence of shear turbulence in a differentially rotating gas–dust disk and of polydisperse solid particles suspended in a carrying flow of solid particles. The defining relations are derived for diffuse fluxes of particles of different sizes in the equations of turbulent diffusion in the gravitational field, which describe the convective transfer, turbulent mixing, and sedimentation of disperse dust grains onto the central plane of the disk, as well as their coagulation growth. A semiempirical method is developed for calculating the coefficients of turbulent viscosity and turbulent diffusion for particles of different kinds. This method takes into account the inverse effects of dust transfer on the turbulence evolution in the disk and the inertial differences between disperse solid particles. To solve rigorously the problem of the mutual influence of the turbulent mixing and coagulation kinetics in forming the gas–dust subdisk, the possible mechanisms of gravitational, turbulent, and electric coagulation in a protoplanetary disk are explored and the parametric method of moments for solving the Smoluchowski integro-differential coagulation equation for the particles' size distribution function is considered. This method takes into account the fact that this distribution belongs to a definite parametric class of distributions. 相似文献
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A. V. Kolesnichenko 《Solar System Research》2011,45(3):246-263
The problem of the influence of vortex helicity on the synergic structuring of cosmic matter in it, as well as the appearance
of the effect of negative viscosity in three-dimensional gyrotropic turbulence, were studied in the framework of the fundamental
problem of simulating the evolution of a rotating astrophysical nonmagnetic disk—in particular, the accretion disk—surrounding
the Sun at the early stage of its existence. The evolution equations for averaged vorticity and vortex helicity, as well as
rheological relations for the turbulent flow of heat and asymmetrical tensor of the turbulent stress in helical turbulence,
were obtained. The demonstrative dependence of helicity on the rotation velocity, density (temperature) gradients, and turbulent
energy of the disk gas was established. The role of helicity in the appearance of the inverse Richardson-Kolmogorov energy
cascade from small vortices to larger ones and the related process of the generation of the power-consuming macroscale coherent
vortex formations appearing in gyrotropic turbulence at high Reynolds number were discussed. The results of the numerical
experiments confirming the real existence of the inverse energy cascade in helical turbulence were analyzed. It was assumed
that the relatively long-term decay of turbulence in the solar protoplanet cloud can be due to the absence of the reflective
symmetry of the anisotropic field of the turbulent velocities with respect to its equatorial plane. As the concept of the
inverse energy cascade in three-dimensional helical turbulence is more and more reliably confirmed in numerical experiments,
accounting for this effect affecting the structure and dynamics of the astrophysical nonmagnetic disk becomes important during
its simulation. 相似文献
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1 INTRODUCTIONThe maing-length theory (MLT) is the most commonly used approach to calculate convective energy transport in stars and other astrophysical situations. Based on the original idea ofPrandtl (1952) that turbulent parcels trallsfer heat in a similar way as molecules of gas do inthermal conduction, the MLT assumes that convection cells, drived by buoyancy, move thlougha ~ng length 1 and release the heat they carry when they merge with their environment. Themost widely adopted f… 相似文献